Here is an abridged version of post five from that thread which hopefully answers your question:

JavaScript is the common term for a combination of the ECMAScript programming language plus some means for accessing a web browser's windows and the document object model (DOM).

JQuery is a JavaScript library that handles many commonly used features and also handles the differences between, e.g., Internet Explorer and standards-compliant browsers. It's something you can use to reduce the amount of work when creating web-based applications.